Causality is a basic organising principle of physics, yet at the interface of quantum theory and gravity causal order itself may become indefinite. Our group develops frameworks in which local operations are described quantum mechanically without assuming any fixed global order between events. The central object in this approach is the "process", which generalises both quantum states and quantum channels and allows for genuinely indefinite causal relations.

This framework captures situations in which events are not ordered as simply “A before B” or “B before A”, even probabilistically, but are related in a genuinely quantum way. It provides the basis for studying causally nonseparable processes, causal inequalities, Bell-type theorems for temporal order, and concrete physically motivated scenarios such as the quantum switch and the gravitational quantum switch. Beyond their foundational significance, indefinite causal structures can also be exploited as quantum information resources, yielding quantum advantages in computation, query complexity, and communication complexity.

Further Reading:

1. O. Oreshkov, F. Costa, C. Brukner, Quantum correlations with no causal order, Nature Communication 3, 1092 (2012)

2. Č. Brukner, Quantum Causality, Nature Physics 10, 259–263 (2014).

3. C. Branciard, M. Araújo, F. Costa, A. Feix, and Č. Brukner, The simplest causal inequalities and their violation, New J. Phys. 18, 013008 (2016).

4. P. A. Guérin, A. Feix, M. Araújo and Č. Brukner, Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication, Phys. Rev. Lett. 117, 100502 (2016)

5. M. Zych, F. Costa, I. Pikovski and Č. Brukner, Bell’s theorem for temporal order, Nature Communications 10, 3772 (2019).

6. M. J. Renner and Č. Brukner, Computational Advantage from a Quantum Superposition of Qubit Gate Orders, Phys. Rev. Lett. 128, 230503 (2022).

7. S. Fedida, A.-C.de la Hamette, V. Kabel, and Č. Brukner, Knot invariants and indefinite causal order, Quantum 9, 1875 (2025).

8. Watch our video clip on causal witnesses